CALC In an L-R-C series circuit the current is given by i = I cos ωt. The voltage am...

CALC In an L-R-C series circuit the current is given by i = I cos ωt. The voltage amplitudes for the resistor, inductor, and capacitor are V_R, V_L, and V_C. (a) Show that the instantaneous power into the resistor is What does this expression give for the average power into the resistor? (b) Show that the instantaneous power into the inductor is What does this expression give for the average power into the inductor? (c) Show that the instantaneous power into the capacitor is p_C = What does this expression give for the average power into the capacitor? (d) The instantaneous power delivered by the source is shown in Section 31.4 to be p = VI cos ωt(cos Φ cos ωt - sin Φ sin ωt). Show that p_R + p_L + p_C equals p at each instant of time.